Nuprl Lemma : sq_stable__ip-triangle
∀rv:InnerProductSpace. ∀a,b,c:Point. SqStable(Δ(a;b;c))
Proof
Definitions occuring in Statement :
ip-triangle: Δ(a;b;c),
inner-product-space: InnerProductSpace,
ss-point: Point,
sq_stable: SqStable(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
ip-triangle: Δ(a;b;c),
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
sq_stable__rless,
rabs_wf,
rv-ip_wf,
rv-sub_wf,
inner-product-space_subtype,
rmul_wf,
rv-norm_wf,
real_wf,
rleq_wf,
int-to-real_wf,
req_wf,
ss-point_wf,
real-vector-space_subtype1,
subtype_rel_transitivity,
inner-product-space_wf,
real-vector-space_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
because_Cache,
lambdaEquality,
setElimination,
rename,
setEquality,
productEquality,
natural_numberEquality,
instantiate,
independent_isectElimination
Latex:
\mforall{}rv:InnerProductSpace. \mforall{}a,b,c:Point. SqStable(\mDelta{}(a;b;c))
Date html generated:
2017_10_04-PM-11_57_58
Last ObjectModification:
2017_03_15-PM-04_58_29
Theory : inner!product!spaces
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